The computer technology used in presently announced transaxial tomography devices is too primitive to handle, in a feasible period of time and at a feasible cost, data obtained either from rapidly moving objects (heart) or large amounts of data covering the whole extent of a big organ (lungs), and to display the results obtained from such data in a truly effective way. The computer technology whose development is being proposed here will pave the way to third generation devices, with capabilites far beyond those of the devices available today. This will be done by (a) improvements to an existing programming system and data base, (b) development of convolution type algorithms for fan-beam and cone-beam geometries, (c) use of optimization techniques, (d) implementation of an operator-interactive graphics system, (e) use of microprogrammed specialized functions for the reconstruction problem. Cooperation with the Mayo Clinic on the design of a dynamic spatial reconstructor for the study of cardiopulmonary disabilities and on early detection of cancer lesions will provide immediate medical application of our work.